A number of dismutation and transalkylation catalysts have already been described in the prior art. Some are based on mordenite, in particular so-called "large pore" mordenites. In United States patent U.S. Pat. No. 3,506,731, the mordenite is in its hydrogen form. This is also the case in U.S. Pat. No. 4,151,120, U.S. Pat. No. 4,1180,693 and U.S. Pat. No. 4,210,770 where the catalyst comprises mordenite in a SiO.sub.2 /Al.sub.2 O.sub.3 ratio which is in the range 10 to 100 and at least one metal selected from the group formed by Ni, Co, Ag and Pd. More recently, U.S. Pat. No. 4,665,258 describes a process for dismutation of a feed containing toluene using a catalyst containing mordenite in an SiO.sub.2 /Al.sub.2 O.sub.3 molar ratio of more than 30, preferably between 40 and 60, more preferably about 48.